Ms. burke invested $53,650, part at 10.5% and the rest at 12%. if the income from the 10.5% investment is one third of that from the 12% investment, how much did she invest at each rate?

$14,800 at 10.5%

$38,850 at 12%

Step-by-step explanation:

Investment at 10.5% (x):

(0.12[$53,650 - x])/0.105x = 3

$6,438 - 0.12x = 0.315x

0.435x = $6,438

x = $14,800

Investment at 12%:

= $53,650 - $14,800

= $38,850

Investments: @ 10.5%, $14,800; @ 12%, $38,850

Proof: (income from 1st is 1/3 that of the income from the 2nd):

= (0.105[$14,800])/(0.12[$38,850])

= $1,554/$4,662

= 1/3

throw the computer

step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.